The role of velocity derivative skewness in understanding non-equilibrium turbulence

doi:10.1088/1674-1056/abbbdc

Abstract

The turbulence governed by the Navier–Stokes equation is paramount in many physical processes. However, it has been considered as a challenging problem due to its inherent nonlinearity, non-equilibrium, and complexity. Herein, we review the connections between the velocity derivative skewness S_k and the non-equilibrium properties of turbulence. S_k, a reasonable candidate for describing the non-equilibrium turbulence, which varies during the non-equilibrium procedure. A lot of experimental or numerical evidences have shown that the perturbation of energy spectrum, which associated with the excitation of large scales, results in an obvious variation of S_k, and S_k is a negative value in this rapid energy decay process. The variation of positive S_k is closely related to the perturbation of transfer spectrum, and this corresponds to the backward energy transfer process. In addition, the skewness characterizes the production (or reduction) rate of enstrophy due to vortex stretching (or compression). Using the transport equation of turbulent energy dissipation rate and enstrophy, it is possible to establish a theoretical connection between skewness and the non-equilibrium turbulence. It is expected that this work could trigger the rapid advancement of the future studies of non-equilibrium turbulence, and also the improvement of turbulence models.

Keywords: velocity derivative skewness non-equilibrium turbulence turbulence model

Received: 10 August 2020
Revised: 20 September 2020
Accepted manuscript online: 28 September 2020

Fund: the National Natural Science Foundation of China (Grant No. 11772032) and the Science Foundation of North University of China (Grant No. 11026829).

Corresponding Authors: ^†Corresponding author. E-mail: feng.liu@nuc.edu.cn

Cite this article:

Feng Liu(刘锋), Le Fang(方乐), and Liang Shao(邵亮)$ The role of velocity derivative skewness in understanding non-equilibrium turbulence 2020 Chin. Phys. B 29 114702

Fig. 1.

Streamwise evolution of S_k in fractal-generated grid turbulence. Different symbols correspond to different transverse locations. S_k reaches an approximately constant at x/M ≈ 20. Reproduced from Ref. [4], copyright 2015, with permission of AIP Publishing.

Fig. 2.

C_ε versus Re_λ for NN and RR cases. NN: normally decaying case (equilibrium); RR: non-equilibrium decaying case, which is produced by reversing all velocities at time 0. Stages I, II, III, and IV represent different time-evolution stages, among which I denotes the ${C}_{\epsilon }\sim R{e}_{\lambda }^{-2}$ stage, IV denotes the non-equilibrium stage. Reproduced from Ref. [35], copyright 2019, with permission of American Physical Society.

Fig. 3.

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